Expert: Ahmed Salami - 8/18/2010

Question
John and Ali together took 5 days to paint their house. If John and Ali worked together for 2 days, followed by John worked alone for 8 days, Ali will take 1 more day to complete the remaining work. How long will John take to pant the house all by himself?

Answer
Hi Raymond,
Lets represent the total amount of work to be done painting the house as Z. And if they can complete it by working together for all of 5 days, lets say John does an amount of work X and Ali does Y.
This means that in a day, John can do X/5 amount of work and Ali can do Y/5, where
X + Y = Z
Now, if they both work for 2 days then they would cover (2/5)Z work already. John working alone for 8 days means he does 8X/5 amount of work and Ali working for 1 day means he does Y/5 of the work.
And so,
2Z/5 + 8X/5 + Y/5 = Z
8X/5 + Y/5 = 3Z/5
8X + Y = 3Z
but
Y = Z - X
therefore,
8X + (Z - X) = 3Z
7X + Z = 3Z
7X = 2Z
X = 2Z/7
which means that John can do 2/7 of the total work in 5 days or (2/7)/5 = 2/35 in a day. He then needs 1/(2/35) = 35/2 i.e 17.5 days to complete the total work all by himself.

Regards